Video Transcript
Given that 𝑧 is equal to five
plus three 𝑖, express 𝑧 over two in the form 𝑎 plus 𝑏𝑖.
We’ve been given a complex
number, five plus three 𝑖, and we’re looking to work out the value or the
complex number given by 𝑧 divided by two. 𝑧 divided by two is five plus
three 𝑖 divided by two. To divide a complex number by a
real number, we need to divide both the real and the imaginary part of the
complex number by that real number. We divide five — that’s the
real part — by two. And we divide the imaginary
part, three, by two. So we see that, for our complex
number, 𝑧 over two is the same as five over two plus three over two 𝑖.
